3:AM Magazine

Reloading Beckett’s philosophical libraries

Eubilides worked in the 4th century BC. His puzzle was popularised by Diodorus Cronus who like Eubilides had “…sophistical leanings, … flamboyancy and … love of showmanship” according to Sedley but who, supposedly, died of shame when he couldn’t solve a puzzle set by some other philosopher in front of the King of Egypt. The sorites became a chief weapon between two schools of philosophy, the Stoa and the Academy. Plato led the Academy in attacking the dogmatism of the Stoa. The sorites was the master puzzle against which the Stoics seemed defeated. The catastrophic power of the puzzle was recognized by Academicians after 273 when Arcesilaus adopted Diodorus’ sorites’ reasoning.

The Stoic reasoner argued for something similar to Descartes’ clear and certain impression. Knowledge was certain clarity. These impressions were considered as having propositional content. The Stoa believed that they were able to pick out truth with complete accuracy. The catastrophe threatened by the sorites is clear: a clear impression can be nibbled away by imperceptibly small subtractions until the certain impression is lost. So far, so Beckettian.

The Stoic response emphasised Beckettian ignorance. Chryssipus became head of the Stoics in about 232 according to Williamson. Chryssipus was considered by the Ancients as the greatest logician of them all according to Barnes. “Unfortunately the two volumes (i.e. scrolls of papyrus) he is known to have written On the Little By Little Argument do not survive; nor do his three volumes On Sorites Arguments Against Words. There are only fragments and reports,” reports Williamson.

Yet what has been reconstructed from these fragments suggests that Chrysippus understood the problem of the borderline in terms of our ignorance, rather than anything about the heap itself. A sequence of questions and answers presumed a monotonic sequence (so no answer of ‘no’ fell between answers of ‘yes’, and vice versa) and the Stoic presumed a principle of bivalence. Logically, there has to be a grain the removal of which turns a heap into a non-heap and a non-heap into a heap. However, for whatever reason, we cannot discriminate in enough fine-grained detail to ever know which grain it is. Even were we to pick out the correct grain we couldn’t know it because the grain next to it would seem just as clear to us as the actual one. We would just have been lucky.

The pattern of responses in the typical sorites shows certainty moving through a smeared zone of uncertainty back towards certainty again. The issue the Stoics had to face was how to respond in the smeary zone. The crisp sharp borderline they knew existed in there somewhere was forever hidden. Chryssipus recommended a strategy of silence. Upon approaching the smear and doubt, his guiding principle was, ‘where knowledge is uncertain, no answer should be given’.

Silence here is not merely ‘not saying’. It is also about ‘not believing’. Beckett inherits this idea about silence. It is linked to what his characters are able to believe. The Stoics held that one should believe only what one knows is correct. The wise person trains her discriminatory powers so she is fooled less than ordinary thinkers. But the sorites confronts even her with indiscriminable impressions that training cannot annihilate. In these cases, judgment must be suspended. She may try acting on plausible assumptions without believing the truth of them in such cases. She is not omniscient but she is infallible, in that, like the Cartesian, her impressions are her own even if they are unbelievable. But Stoics doubted the existence of such wise people. They were an ideal.

As Williamson explains, in order to avoid error of thought and speech Chryssipus recommended that “… at some point in the sorites interrogation one should fall silent and withhold assent… If the source of the puzzle is just that one does not know whether ‘yes’ or ‘no’ is the right answer to some of the questions, it turns out to be on a level with other matters of which one is simply ignorant… Why should such an honest admission of ignorance not completely dissolve the puzzle.” The profound silence of Chryssipus is the silence of fallibility, of ignorance, of the futility of going on and trying to answer something that is unknown. Beckett’s silence is a Chryssipean inheritance.

But an explanatory step is missing in this analysis. Why does Chryssipus recommend silence rather than the admission ‘I don’t know.’ It is because of a crucial feature of the structure of vagueness. Not only is it unclear where the actual sharp borderline between heap and non-heap lies, it is also unclear where the sharp borderline between clear and unclear is as well. In other words, not only don’t we know where the last grain of a heap is, nor do we know where the last grain we are certain is a heap is either. The borderline of the smeary borderline is susceptible to the same troubling reasoning faced trying to locate the original borderline. ‘Heap’ is sorites susceptible, and so is ‘clear heap’. And so is ‘clearly clearly heap’. The iteration threatens to stretch out infinitely. Philosophers have labelled this feature ‘higher order vagueness’.

Chryssipus is ignorant of the borderline of his ignorance, and ignorant of the borderline of the borderline of that ignorance. This ‘higher order’ iteration is echoed throughout Beckett. On the principle that we should assert nothing false, his silence preserved this principle. Silence didn’t assert knowledge of ignorance, it asserted nothing. Indeed, to ensure that the principle of refusing to assert what is not clear, Chryssipus recommends that silence begin at a place before certain uncertainty. This squeezes the scope of certainty, reducing it. The more maniacally followed, the recommendation makes ever less assertible. The complexity of the sorites threatens to erode, little by little, what can be thought, what can be said. The delicacy of the situation, its precariousness, results in an expanding blindspot.

The sceptic Carneades thought Chyrissipus’ strategy no better than a refusal to play the next move in a game, or like falling to sleep. ‘Why should your pursuer care whether he traps you silent or speaking?’ he asks. Beckett’s texts speak to the contempt of the sceptic; the wreckage of humanity is working perfectly and yet cannot speak into the vagueness not even Beckett fully understands if, as is likely, he didn’t understand the implications of the sorites. As Gontarski notes, “Clov’s opening speech is motivated by some barely perceptible change that he perceives while inspecting his environment. In the Riverside notebook Beckett writes: ‘C perplexed. All seemingly in order, yet a change'”. And it helps explain the sequential patterning that is essential to Beckett’s aesthetic.

The precariousness of Chryssipus’ position is in answering the sceptic who wonders why she might not then suspend judgment over all cases, clear and unclear. Chryssipus is, as Williamson neatly puts it, “in a very delicate position. He stops at clear cases, avoiding the risk of giving answers that are not clearly correct only at the cost of failing to give answers that are clearly correct (in the Stoic sense).”

Carneades argues against the existence of Stoic Gods using a little by little argument that patterns itself differently from the classic formula but is still nevertheless recognisably a sorites. “If Zeus is a God… Poseidon too, being his brother, will be a God. But if Poseidon (the sea) is a God, the (river) Achelous too will be a God. And if Anchelous is, so is the Nile. If the Nile is, so are all rivers. If all rivers are, streams too would be Gods. If streams were, torrents would be. But streams are not. Therefore Zeus is not a God either. But if there were Gods, Zeus too would be a God. Therefore there are no Gods.” Silence in the face of this fierce reasoning against Stoic rational theology is inadequate to resist non-arbitrarily any step of the argument.

The problem is conceived in terms of disputations about the premises of the argument, rather than the argument form itself, which was regarded as being valid. The sorites became a focus of dispute between Dogmatic/rationalist doctors and Empiricist ones. How many observations were enough to make it reasonable to suppose a certain cure? The sorites threatened the common-sense idea of ‘enough’. Galen and the Empiricist doctors reasoned that the sorites would dispute the existence of flocks, herds, nations, crowds, boyhood and seasons. They argued that something was wrong with the sorites argument, although they didn’t know what.

Beckett’s familiarity with the sorites was such that he knew of samples outside of philosophy. Horace defends young poets using sorites against the idea of ‘old poets’ in the Epistle to Augustine (II.i, 47). The attraction of Horace for Beckett lay in his timidity at Philippi, and, according to Ackerley “…by what Lempriere regrets, licentious expressions and indelicate thoughts.” Horace’s ratio ruentis acetvi, Clov’s ‘impossible heap’, emanates from the ‘amiable madness’ he references in his study of Proust from Schopenhauer.

My claim, however, is more than that Beckett drew on elements of the sorites puzzle. He presents the sorites in terms of a theory-particular answer to the puzzle rather than in general terms. In Watt there is a sustained passage where the sorites characterised as an ‘epistemic’ solution to vagueness makes better sense of the passage than all other attempts to characterise it. Consider this: “The sun on the wall, since I was looking at the sun at the wall at the time, underwent an instantaneous and I venture a radical change of appearance. It was the same sun and the same wall, or so a little older that the difference may safely be disregarded, but so changed that I felt I had been transported, without my having remarked it, to some quite different yard, and to some quite different season, in an unfamiliar country…”

Notice that the change is ‘instantaneous’ rather than a gradual transformation. The epistemic conception of the sorites is precisely that there is, in fact, an exact and precise borderline, contrary to everything that seems to be the case. So ignorance of the truth causes the problem, not absence of borderlines or ideterministic language or thought. A commitment to bivalence, the principle that every proposition is either true or false, is at the heart of classical logic and the epistemic approach preserves classical logic and thus this commitment. That Beckett presents the mystical experience described here in Watt as ‘instantaneous’ suggests that he wasn’t presenting a deviant logic to the situation but was rather holding on to the classical in order to dramatise the absurdity of the truth. He punches through to the other side of the sorites blindspot and introspects the unintrospectable transition. This accounts for the mystical feel.

Given that Beckett misidentified what the sorites was a puzzle about he was in a sense writing blind. But Watt can now be read in terms of its solution given in terms of our ignorance of the actual sharp borderlines that our thought and language cannot discover. The madness of the scene is one that reveals a character knowing the unknowable. The hole he drills reveals that strange absolute changed sameness which baffles coherence and us with the vertiginous sensation of borderless transition characteristic of vagueness.

Other theories of vagueness reject sharp boundaries. Deviant logics have been applied to the sorites. Many valued logicians and fuzzy logics argue that if a two value logic claiming that every proposition is either true or false can’t handle the situation, then introduce more values. But the philosopher Mark Sainsbury remarks that “you do not improve a bad idea by iterating it.” The approach fails to handle thoughts such as hedging which allows us to hover between being decisive because each disjunct is assigned equal value. Yet asserting equal disjuncts should increase the truth value of the statement, but many valued logic can’t register this because it only assigns its truth value to the most probable claim. Equal disjuncts don’t increase the assigned value.

Supervaluationists such as Kit Fine argue that the statements in the smeary borderline lack truth values. This position therefore proposes that there is a truth-value gap at the point where Chryssipus falls silent. Fine and David Lewis conceive of vagueness in terms of a massive hyper-ambiguity. The claim is that there is no settled agreement about which language is being used and so tiny differences between languages sets up the indeterminism in the borderline cases. Roy Sorensen summarises the position: “Instead of there being one vague concept, there are many precise concepts that closely resemble each other. ‘Child’ can mean a human being at most one day old or mean a human being at most two days old or mean a human being at most three days old …. Thus the logic of vagueness is a logic for equivocators.” Propositions that are considered true on all disambiguations are true. But as Michael Tye argues, disambiguation is usually done before assessing the truth value of any proposition. How else do you know whether what is being said is true or not if you haven’t decided yet what is being said? Mixed interpretations is a feature of ambiguity but not vagueness.

Supervaluation approaches retain an appearance of bivalence because it can say that every proposition must be true or false. But by reversing the order of disambiguation (doing it after assigning truth values) the claim is a non-substantive one for any borderline case. And other features of the classical logic repertoire are lost. Tarski’s Convention T makes truth disquotational, which is the claim that states that “a statement S is true iff S”. So, for example, ‘A thousand grains of sand make a heap’ is true if and only if a thousand grains of sand make a heap. Supervaluationists think that truth is ‘true under all precisifications’ and they call this ‘supertrue.’ But if they accepted Convention T then supertrue would be disquotational. Williamson argues that the supervaluationist would be committed to saying P is either supertrue or not-P is supertrue, which in turn would commit them to either P is true or Not P is true. Supervaluationists would have then lost their truth-value gap.

Sorensen, who is with Williamson the leading philosopher arguing that vagueness is about our ignorance of the sharp borderlines rather than any fault in our language, accuses the supervaluationist of ontological dishonesty. As part of his solution to the sorites paradox, the supervaluationist will assert, ‘There is a human being who was a child when n days old but not when n + 1 days old’. For this statement comes out true under all admissible precisifications of ‘child’. However, when pressed the supervaluationist will add an unofficial clarification: ‘Oh, of course I do not mean that there really is a sharp threshold for childhood’. For Sorensen the dishonesty runs deep: the supervaluationist position hides nihilism.

Peter Unger in 1979 argued that the sorites dissolved the coherence of all vague terms. Given that nearly everything is sorites susceptible, the position resulted in the rejection of more or less everything. The corrosive force of this position is where one might expect Beckett’s sympathies to lie. The nihilist sorites denies the base step of the argument. If reason can show that a single grain is a heap and also prove it isn’t then there is something inherently absurd in the very idea of a heap. The nihilist courageously faces the consequences of the extreme position and the world is annihilated. All that is left is at best an ‘as if’ universe. For pragmatic reasons we may continue to talk as if heaps and bald men exist but it is merely a convention to retain a thread.

But vagueness is vague. The nihilist proves that vagueness doesn’t exist. Therefore an argument depending on it can’t exist either. The nihilist is a self-defeater. If vagueness exists then it cannot. But perhaps the self-defeater is an argument for the impossibility of asserting the nihilist position, and perhaps this is what Beckett anticipates will come oozing through the hole he is drilling through language. The seminal work of Roy Sorensen from his 1988 classic study of Blindspots have drawn attention to the varieties of this phenomenon where truth is inaccessible, even unknowable.

An important moment in revitalising interest in this phenomenon was in the discovery of a type of sentence discovered by G.E. Moore, one of the founders of Analytic philosophy, at about the same time Beckett was writing Murphy and Watt. “It is raining but I do not believe it,” is the sentence of 1943. It is an example of a sentence that is quite possibly true, is grammatical, logical but, nevertheless, unassertable. Fitch proved that there are unknowable truths in 1963. Williamson thinks of this discovery as an embarrassment not a paradox.

Moore was the March Hare in the John Tenniel depiction of The Mad Hatter’s Tea Party (J.M.E. McTaggert was the dormouse, Bertrand Russell the Mad Hatter) and the threesome were known as the Mad Tea Party of Trinity according to Wiener. His strange sentence is only strange given current background assumptions brought about by a critique of Hegelian idealism led by Moore and others. Idealism denies unthinkable truths. The sentence was the one discovery that impressed Ludwig Wittgenstein and brooding on it helped formulate the extreme positivism of the Tractatus.

The sentence is an example of a pragmatic paradox philosophers label the counterprivate. They link it to the introspective turn in philosophy that is associated immediately with Descartes but is perhaps first elaborated in Augustine who wrote, “I am not at all afraid of the Academicians, who say What if you are deceived? For if I am deceived I am. For he who is not, cannot be deceived, by this same token I am. And since I am if I am deceived, how am I deceived in believing that I am? For it is certain that I am if I am deceived. Since, therefore, I, the person deceived, should be, even if I were deceived, certainly I am not deceived in this knowledge that I am. And consequently, neither am I deceived in knowing that I know. For, as I know that I am, so I know this also, that I know.” Beckett’s interest in the Cartesian introspective project is well-documented.

Sorensen draws out the closeness of the Augustinean and the Cartesian project. He writes about Descartes in opposition to Descartes’ own self-representation. Descartes thought of himself as a revolutionary, breaking away from his Catholic background and education. Sorenson argues that Descartes was actually continuing in the introspective tradition of Augustine. He endorses Miles Burnyeat’s contention that Augustine was the first philosopher to make the subjective–objective distinction. For Beckett, the introspective writer par excellence, this genealogy is pertinent.

The linguistic nihilist presumes all vague terms are merely pseudo-terms. They are self-defeaters. The metaphysical nihilist assumes that all vague predicates exist but are empty. ‘Heap’ is like ‘empty full’. There is a third option but it has never been taken, which is to apply vague predicates to everything. Nihilist incoherence requires no drilling. The epistemic approach does.

Alternatively, maybe Beckett is appealing to a form of contextualism. Indexicality is the culprit (e.g. ‘I am always here’ etc). The influence of the Heraclitean thesis that ‘all is flux’ is important to Beckett elsewhere. Beckett read Heraclitus in the 1930s and is suggested by Estragon’s contention that ‘everything oozes’ and in Murphy where the line from his Windelband volume is raised where according to Gontarski the short circuit of love requited confutes the Heraclitean principle of “…the circuit completed by matter of its successive changes in the universe” (quoting from Windelband). Just as each assertion on separate days that “tomorrow Godot will come” is not identical with any of the other assertions, the uniformity of the sentence used to make the assertion may fool the unwary or novice language user. Contextualists may insist on the truth of each inductive step whilst equivocating as to whether what each step means is identical with its predecessor or successor. In this way the sorites series is reduced to a series of indexicals that denies that any induction step can ever be falsified.

Scott Soames argues that all vague terms are indexical and Hans Kamp argues that vague words work like satellites orbiting the store of the linguistic commitments of the sorites-monger. Diane Raffman argues that sorites work using a gestalt psychology, so sorites series are triggered shifts between look-alikes. Stewart Shapiro takes a notion prevalent in legal debates, developed from Waissman and popularised by H.L.A. Hart, of ‘open texture’. Language is open textured in that “every description stretches, as it were, into a horizon of open possibilities: However far I go, I shall always carry this horizon with me.” This position is used to justify discretion when judging borderline cases. Delia Graff relativises to an American pragmaticism. Practical interest relativises meanings and produces enough shiftiness to prevent a sorites series.

Sorensen complains that contextualists end up with too much shiftiness. “Analogy: hydrologists agree there is much hidden water but all hydrologists are scientifically committed to denying Thales’ claim that all is water,” he says. He also argues that some sorites are just too damn complex for the sort of homespun equivocation contextualism deals in. A billion, billion, billion iterations of Godot may be embedded in a sorites that never could generate the required context shifts. Sorenson remorselessly drills home his complaint: “More fancifully, there could be a vague predicate that instantly kills anyone who thinks about it.”

Beckett did indeed have doubts about the stabilising anaphoric resources of language. He did feel the existential unease of both the nihilist and the Heraclitean, where his sympathy is with Holderlin’s lines, “…suffering humanity perishes and falls blindly from one hour to the other, like water dashed from crag to crag year after year, down into the unknown.” But it is through the resources of classical logic that the sorites has been understood as a problem of ignorance, and human fallibility. Beckett takes ignorance to be an essential aspect of the human condition. He gropes blindly towards the epistemic solution to the sorites rather than via deviant logics, nihilism or contextualism.

Beckett shows the madness of classically behaving language. The epistemic solution is the only approach to the sorites which assumes classical bivalence – the principle that a proposition is either true or false – in a way that the unavoidable incredulity of the solution is fully grasped. As we’ve seen, supervaluation does so but only by assigning truth values before deciding which particular language they’re speaking. The epistemic solution decides which language its speaking and then commits to bivalence. So there has to be a sharp cut off point, and so the fault lies in us. We are absolutely ignorant of where the sharp cut-off point is. The solution is rightly greeted with incredulity by competent language users because it seems to violate a tautology but is actually a blindspot.

Remember that Beckett didn’t know that this was what he was introducing into his texts because, by following Windelband’s lead, he misidentified the paradox’s nature. Had Beckett been reading contemporary philosophers of his time then he might have picked up some of this stuff. But given that from what we know he was reading overviews, summaries and classics, it is unlikely that a non-specialist would have had contact with this material. So although the philosophical analysis of the sorites has been a central concern for analytic philosophers throughout the last century, and in particular since the mid 1970s following Michael Dummett’s seminal paper, Wang’s Paradox, Beckett didn’t know anything about it.

And it’s likely that he only touched on it through the originators because of his interest in the PreSocratics. Throughout the medieval period little was written about the sorites. It did reappear in the Renaissance in the guise of the literary pursuit of humanist rhetoric. The Roman Epicurean-Christian humanist Lorenzo Valla was a key figure in reconstituting the sorites as a valid form of argument. But sorites puzzles were relatively unimportant, although Leibniz referred to both the heap and the bald man in arguing with Locke in the seventeenth century.

The rejection of Hegelian idealism and consequently the rejection of its rejection of the law of the excluded middle at the end of the nineteenth century was supported by the development of logic by Frege and Russell. Logic, like science and maths, required precision. Consequently, as Williamson vividly puts it, “vagueness, like madness, must be mentioned in order to be excluded.” Russell and Peirce produced theories of vagueness and the value of precision was developed as a key value. Natural language was presented by Frege as deficient. Frege conceived of vagueness as incomplete definition. But if Beckett’s reading remained influenced by Hegelianism then it is unlikely that he could have even considered vagueness in the terms now considered fruitful by contemporary philosophers.

The recent work, by Williamson and Sorensen in particular, has reclaimed some of the original ideas about the sorites found in Chryssipus, that vagueness is ignorance of sharp borderlines, not absence of sharp borderlines through incomplete, faulty or for some other reason indeterminate language and thought. Of course, the claim that Chryssipus was an epistemicist is not uncontested. Susanne Bobzien has recently argued in particular against Williamson’s conclusion about the Stoic, suggesting that he was more of a supervaluationist than Williamson accepts. And Roy Sorensen would probably argue that Williamson is more of a supervaluationist than he would accept.

But given Beckett’s conception of his creative process as one of impotence and ignorance – whereby the impotence is harnessed to the ignorance – the sorites is being approached as a vehicle for his ignorance-based impotence. It is an idea that in turn buckles the sorites puzzle to his ethic of ignorance derived from his study of Arnoldus Geulincx, the seventeenth century Flemish metaphysician and philosopher. In Murphy there is a reference to the “beautiful Belgian-Latin” of Geulincx’s “Where you are worth nothing, there you should want nothing”. What better than a puzzle whose solution renounces knowledge and insists on unbelievability. As a principle organising the “stains on the silence” that he considered his texts to be, this blindspot approach would have immense appeal to the writer who saw artistic calling in terms of efficient disobedience.